10.35.10.6 Execution of Propagating Indexicals

Consider the definition of a constraint C containing a
propagating indexical X in R. Let
TV(X,C,S) denote the set of values for X that can make
C true in some ground extension of the store S.
Then the indexical should obey the following coding rules:

all arguments of C except X should occur in R

if R is ground in S, S(R) = TV(X,C,S)

If the coding rules are observed, S(R) can be proven to contain
TV(X,C,S) for all stores in which R is monotone. Hence
it is natural for the implementation to wait until R becomes
monotone before admitting the propagating indexical for execution. The
execution of X in R thus involves the following:

If D(X,S) is disjoint from S(R), a contradiction is detected.

If D(X,S) is contained in S(R), D(X,S) does not
contain any values known to be incompatible with C, and the
indexical suspends, unless R is ground in S, in
which case C is detected as entailed.

Otherwise, D(X,S) contains some values that are known to be
incompatible with C. Hence, X::S(R) is
added to the store (X is pruned), and the indexical
suspends, unless R is ground in S, in which case
C is detected as entailed.

A propagating indexical is scheduled for execution as follows:

it is evaluated initially as soon as it has become monotone

it is re-evaluated when one of the following conditions occurs:

the domain of a variable Y that occurs as dom(Y)
or card(Y) in R has been updated

the lower bound of a variable Y that occurs as min(Y)
in R has been updated

the upper bound of a variable Y that occurs as max(Y)
in R has been updated